Analogy and Structure

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Analogy and Structure provides the necessary foundation for understanding the nature of analogical and structuralist (or rule-based) approaches to describing behaviour. In the first part of this book, the mathematical properties of rule approaches are developed; in the second part, the analogical alternative to rules is developed. This book serves as the mathematical basis for Analogical Modeling of Language (Kluwer, 1989). Features include: A natural measure of uncertainty: the disagreement between randomly chosen occurrences avoids the difficulties of using entropy as the measure of uncertainty. Optimal descriptions: the implicit assumption of structuralist descriptions (namely, that descriptions of behaviour should be correct and minimal) can be derived from more fundamental statements about the uncertainty of rule systems. Problems with rule approaches: the correct description of nondeterministic behaviour leads to an atomistic, analogical alternative to structuralist (or rule-based) descriptions. Natural statistics: traditional statistical tests are eliminated in favour of statistically equivalent decision rules that involve little or no mathematical calculation.